(Transcript of the lesson commentary.)
Plasma in stellar energy generators
The name stellarator is derived from the Latin stella, which means star, and the English word generator — so it is a generator of stellar energy. And indeed, experiments on these devices attempt to imitate the nuclear reactions taking place in stars. According to the definition, it is a device designed to maintain plasma using a specially shaped magnetic field in order to achieve controlled thermonuclear fusion. Most likely, it will be the fusion of deuterium and tritium nuclei to form helium while releasing a large amount of energy in the form of neutrons.
The original idea behind the stellarator was based on the assumption that the plasma could be held in the reaction space by a specially shaped, helically wound magnetic field that is generated exclusively by external magnetic coils of various shapes. Keeping the plasma free of electrical current allows the stellarator to operate in a steady state. From the first figure eight-shaped stellarators, through to the oval shape, the development has recently been towards stellarators with a toroidal chamber shape with an additional winding that provides the necessary magnetic twist.
One way to keep fusion fuel heated to temperatures exceeding hundreds of millions of Kelvins is to enclose it in a magnetic cage formed by a magnetic field of specially shaped coils. The fuel, in the form of plasma, consists of electrons and ions that move helically along magnetic field lines. Thus, in the case of a toroidal shape, where the field lines have a circular path, the particles should circle around endlessly. But for geometric reasons it is obvious that the thread of the toroidal coils will be denser on the inner side of the torus and the magnetic field will be stronger than the field on the outer edge of the torus. The result of such a non-uniform magnetic field can be the drifting of particles across the field, the separation of charges and the creation of an electric field that eventually pushes the plasma out of the torus. To overcome this field, the particle must be forced to spiral around the torus. In stellarators, additional coils take care of twisting the field, enabling helical winding.
The confinement time of the plasma in the twisted magnetic field of stellarators is primarily determined by the possibilities of its heating. With the continuous heating of the plasma, the stellarator could thus work in continuous and steady operation. One of the possibilities for heating the plasma is the use of high-frequency electromagnetic waves, which transmit the necessary energy to electrons and, through collisions, to larger ions. Another possibility is neutral beam injection, during which accelerated neutral particles are fired into the plasma, which then transfer their energy to the plasma particles.
Development and modification of stellarators
The first stellarator was already built in 1953 by the American physicist Lyman Spitzer at the Princeton Laboratory of Plasma Physics as part of the Matterhorn project. Made from a borosilicate glass tube bent into a three-dimensional figure eight and wrapped around magnetic coils, this Model A proved that the stellarator concept worked and that plasma could be created and sustained this way. Another Spitzer Model B achieved a plasma temperature of around 100,000 Kelvin using ohmic heating but only for a very short time. One of the B-series models was already equipped with a divertor that improved the purity of the plasma and reduced the heat loss of the stellarator. In the subsequent, even larger Model C, the injection of neutral particles generated by an external accelerator was first used to heat the plasma in 1964 and five years later a plasma temperature of approximately 5 million Kelvin was achieved.
With the development of stellarators, the figure eight shape changed to an oval shape with toroidal and additional helical windings, which provide the necessary twisting of the magnetic field. The coils of the additional winding of classic stellarators are usually wound around the body of the torus and are thus located below the toroidal and poloidal coils. The additional coils must operate in pairs with the opposite direction of electric currents. In some stellarators, the continuous helical coils are replaced by several intricately shaped individual coils that together create a similar magnetic field.
One or two pairs of such simple continuous coils helically wrapping around the torus, supplemented by poloidal coils are used by the torsatron — one of the modifications of the classic stellarator. The design of the torsatron is based on the assumption that a toroidal field can only be generated using helical coils with identical current direction. The first device of this type, Saturn-1, began operation in 1970 at the Kharkov Physical and Technical Institute.
A similar type of stellarator to the torsatron is the heliotron, which uses yet another set of coils, located off-axis to the torus. A heliotron design with various combinations of helical, toroidal and poloidal coils was investigated at Kyoto University in Japan. Thanks to all the coils, which can have various crooked to bizarre shapes, the plasma in the heliotron finally has the exact desired shape of a coiled ribbon with a changing bean-like cross-section.
Another modification of the stellarator, called the Heliac, is based on the idea of replacing the additional helical windings around the plasma with plasma helically coiled around the poloidal coil. The original Heliac consists only of circular coils, the flexible one adds a small helical coil that allows changing the twist of the magnetic field and plasma.
The latest modification is a helical advanced stellarator called Helias, combining toroidal coils and helical coils into one optimized set of modular coils. Although modular coils have a very complex geometry, they are generally more compact and enable later optimization of the magnetic field. This configuration can be considered the most promising type of stellarator device for a future power plant.
Structural elements of stellarators
In the designs of different types of stellarators, two elements are particularly important: the coils that create the magnetic field to maintain the plasma and the vacuum vessel in which the plasma is maintained during the operation of the device.
Stellarators are characterized by helical coils wrapping around a torus or their equivalent in the form of separate, oddly shaped modular coils that replace them. Depending on the configuration of the stellarator, these special coils can still be combined with classic toroidal or poloidal coils. The three-dimensional shapes and constructions of the modular coils are designed with the help of powerful computers to achieve the best possible magnetic cage and plasma confinement, thus reducing particle losses and various instabilities to a minimum.
The requirements for the design and manufacture of the coils are huge, dozens of coils must be attached with millimeter precision on a solid, stable structure. The correct magnetic configuration is then created by the correct calculation, production and installation of the coils and the appropriate setting of the currents flowing through the coils. To reduce power consumption, the coils of large stellarators are superconducting.
The vacuum chamber surrounding the plasma has a peculiar and irregular shape, resembling a crumpled hollow steel doughnut. The exact shape of the vacuum chamber depends on the type of magnetic configuration each device uses. Numerous magnetic coils located close to the vacuum chamber provide only limited access to the vessel. For the purpose of maintenance, diagnostics and connection of various pipelines and heating, it is provided by ports — channels of different cross-sections located between the windings of the coils.
To protect against high plasma temperatures exceeding 100 million Kelvin, the inner surface of the vacuum chamber is covered with carbon tiles with active water cooling. On the outside of the chamber, on the other hand, there are relatively close superconducting magnetic coils, which must be maintained at a temperature of only 4 Kelvins. To minimize heat transfer from the plasma to the coils, the outside of the vessel is covered with thermal insulation and a deep vacuum is maintained between the vessel and the coils, kept in a giant cryostat.
The magnetic field lines are arranged at the edge of the plasma inside the vessel in such a way that they form small islands — local magnetic traps, in which possible impurities are captured, which are mainly atoms with higher atomic numbers. Captured waste is directed to the divertor. These are special collection plates with a shape copying the curved outline of the edge of the plasma, under which the vacuum pumps are located. Because this device uses magnetic islands, it is called an island diverter.
In a fusion power plant, stellarators using the reaction of deuterium with tritium will still need to have about 1 metre thick neutron shielding between the plasma and the walls of the vacuum vessel or coils. The shielding will also serve as a tritium breeder, capturing neutrons in lithium and producing the desired fuel — tritium. Installation of neutron shielding will lead to moving the magnetic coils away from the plasma, thus requiring more powerful magnets and increasing the size of the entire device.
The most interesting stellarators
Although the original idea of stellarators is more than half a century old, after the initial enthusiasm and subsequent problems with practical implementation, it was necessary to wait for the improvement of computing technology and new findings in the field of plasma behaviour to renew the interest in stellarators. Today, mathematical methods simulating the properties of magnetic fields are accurate enough that the complicated coils and vacuum chambers of stellarators can be designed and manufactured with great precision.
In contrast to hundreds of tokamaks, there are only about 13 experimental stellarators in the world. Among the largest and most important belong the Wendelstein 7-X in Germany, the Large Helical Device in Japan and the Helically Symmetric eXperiment in the USA.
Wendelstein 7-X is an experimental modular facility of the Max Planck Institute for Plasma Physics located in Greifswald, Germany. It is a Helias-type stellarator and is composed of a set of 50 non-planar and twenty planar superconducting coils surrounding a vacuum chamber and creating a magnetic field with fivefold symmetry. This symmetry arises because the entire magnetic system consists of five identical modules, each module containing ten coils. The coils are made of niobium-titanium superconductor, are cooled by liquid helium to a temperature of 4 Kelvin and are capable of creating a magnetic field of up to 3 Tesla. Each coil weighs approximately 6 tons and is about 3.5 metres high. The first Wendelstein 7-X plasma was ignited at the end of 2015.
In addition to the superconducting coils, the main components of the stellarator are a vacuum chamber with a divertor, a cryostat and plasma heating systems. The vacuum chamber has an outer diameter of 16 m, a height of approximately 4.5 m and an almost circular cross-section with a diameter of 4.5 m. It is assembled from 20 parts and includes 254 ports — openings and channels for heating the plasma and complete diagnostics. The created plasma has a main radius of 5.5 metres and contains 5—30 milligrams of fuel, which is a mixture of hydrogen and deuterium. The entire facility weighs 725 tons.
The plasma volume of 30 m3 is heated by the combined effect of a neutral beam injection and electron cyclotron resonance heating with a total heating power of 14 MW. In the Wendelstein 7-X, record values for energy stored in plasma have already been achieved. The value of 6 × 1026 K.s/m3 became a new world record for stellarators.
With strong microwave heating, the energy content of the plasma exceeded one megajoule for the first time without the vessel wall getting too hot. Experiments in the stellarator are gradually leading to the goal set by scientists, which is proof that a stellarator with a plasma temperature of 100 million degrees and discharges lasting up to half an hour is suitable for use in a future thermonuclear power plant.
The second largest superconducting stellarator in the world is the Large Helical Device belonging to Japan’s National Institute of Nuclear Fusion Science, located in Tokyo, Gifu Prefecture, Japan. This major stellarator uses a heliotron magnetic field originally developed in Japan. The magnetic cage consists of a pair of helical outer coils wrapped around a toroidal vacuum chamber, supplemented by three pairs of poloidal coils. The resulting magnetic field gives the plasma inside the shape of a coiled ribbon. The first plasma was ignited in this stellarator in March 1998.
The entire stellarator apparatus weighs approximately 1,500 tons and is housed in a cryostat with an outer diameter of 13.5 metres and a height of around 9 metres. Each of the two helical coils weighing 120 tons, is wound with niobium-titanium superconducting wires and is capable of generating a magnetic field of up to 4 Tesla at the centre of the plasma. The vacuum vessel of the stellarator was divided into 140 parts during assembly and welded in place until the two helices were carefully and precisely installed.
In the Large Helical Device, a plasma ring with a volume of 30 m3 and a radius of 3.9 metres can be heated using three devices with a total heating power of up to 36 MW. In addition to the most powerful neutral beam injection, ion cyclotron radiofrequency heating and electron cyclotron resonance heating are also used. The LHD stellarator holds the stellarator record with a plasma temperature reaching 120 million Kelvin and a pulse duration of almost one hour.
The third interesting facility is the Helically Symmetric eXperiment stellarator, located at the Department of Electrical and Computer Engineering at the University of Wisconsin-Madison in the USA. It is considerably smaller than the first two described stellarators but it is the only device in the world that has a quasi-helically symmetric magnetic field structure. This means that its magnetic cage is axisymmetric, which ensures less leakage of particles from the plasma and makes it easier to heat it to thermonuclear temperature. It has been in operation since 1999.
The 0.44 m3 plasma is maintained by a set of 48 modular twisted coils. Their three-dimensional shapes have been designed by powerful computers to be optimized for generating quasi-helically symmetric fields. In the HSX stellarator, fourfold symmetry is used and the magnetic field reaches a value of 1 Tesla in the centre of the plasma column. The vacuum chamber is made of stainless steel and essentially replicates the complex magnetic geometry of the stellarator.
The plasma is heated using electron cyclotron resonance heating. Two gyrotrons have a total heating capacity of 200 kW. The maximum plasma temperature of up to 30 million Kelvins was achieved on the HSX stellarator.
